- Email: [email protected]
Friction behavior of quenched and tempered steel in partial and gross slip conditions in fretting point contact
Wear 267 (2009) 2200–2207
Contents lists available at ScienceDirect
Wear journal homepage: www.elsevier.com/locate/wear
Friction behavior of quenched and tempered steel in partial and gross slip conditions in fretting point contact A. Pasanen a , A. Lehtovaara a,∗ , R. Rabb b , P. Riihimäki a a b
Mechanics and Design, Tampere University of Technology, P.O. Box 589, 33101 Tampere, Finland Research & Development, Wärtsilä Finland Oy, P.O. Box 244, FI-65101 Vaasa, Finland
a r t i c l e
i n f o
Article history: Received 30 September 2008 Received in revised form 20 March 2009 Accepted 24 March 2009 Available online 7 April 2009 Keywords: Friction Fretting fatigue Fretting wear Partial slip
a b s t r a c t Tangential traction caused by friction in contacting surfaces is a major factor in fretting fatigue that increases stress levels and leads to a reduction in fatigue life. Friction in fretting contact was studied in partial, mixed and gross slip conditions on quenched and tempered steel. Measurements were made with sphere-on-plane contact geometry for polished and ground surfaces. Friction was evaluated from on-line energy ratio and, after the tests, from wear marks. A maximum friction coefficient of over 1.0 was measured at mixed slip zone with polished surfaces, whereas ground surfaces promote lower values in similar operating conditions. The friction coefficient dependence on load cycles and loading frequency is also presented and briefly discussed. The friction data and understanding thus gained is to be used for evaluation of crack initiation with the numerical fretting fatigue model. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Fretting may occur between any two contacting surfaces where short amplitude reciprocating sliding is present over a large number of cycles. This oscillatory movement can take place at the micrometer level, even without gross sliding of the contacting surfaces. This causes fretting wear of the surfaces and fretting fatigue, which can lead to a rapid decrease in fatigue life. Fretting wear is related to surface degradation processes and it can be detected by the appearance of wear debris. The appearance and severity of fretting fatigue is essentially dependent on the stress field on a contact (sub)surface caused by external bulk and contact loading. This stress field, affected by the oscillatory movement of the contacting surfaces, promotes crack nucleation. An extensive description of the fretting phenomenon and its associated contact mechanics is given in Refs. [1–3]. Fretting risks are known to be high in industrial machine components such as medium speed diesel engines, where the contact surfaces have to transfer high tractions. Fretting often occurs in contacts which are designed to be nominally fixed, such as interference fits and screw joints. Fretting fatigue may cause hazardous and unexpected damage in machine components, because the appearing nominal stress levels can be low and the damage that initiates on the inside of the contact cannot be detected by normal visual inspection without opening the joint.
∗ Corresponding author. Tel.: +358 3 311511; fax: +358 3 31152307. E-mail address: arto.lehtovaara@tut.fi (A. Lehtovaara). 0043-1648/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2009.03.047
Proper design, material properties, different kinds of palliatives and surface treatments have been considered as ways to eliminate or control fretting. The promotion of compact and reliable calculation and design rules for fretting requires both modelling and experimentation, due to the complexity of the problem. Modelling provides a detailed understanding of the stress fields and the estimated cracking risk based on multi-axial failure criteria at contacting surfaces and contributes to the design and evaluation of experimental fretting fatigue tests [4–6]. The oscillatory tangential movement of the contacting bodies is the basis of the fretting phenomenon. This causes the tangential traction into the contact, which is known to have a very strong impact on the stress field and thus on cracking risk. The level of the tangential traction is firmly controlled by friction between contacting surfaces and therefore the determination of the friction coefficient in fretting contact is a crucial task. This input value is one of the main uncertainties when the cracking risk of the fretting contact is evaluated with numerical fretting models. The vast majority of the fretting studies have been conducted on gross sliding conditions, where the whole contact is sliding. In such cases, the friction coefficient can be defined simply by dividing the tangential force by the normal force. However, fretting fatigue and corresponding crack formation is known to take place primarily in partial or mixed slip conditions, where tangential force is less than or just reaching the product of friction coefficient and normal force. This complicates the determination of the friction coefficient. Prediction of the slip zone friction coefficient by using measured mean friction coefficient is given in reference [7]. A detailed approach for measurement and analysis of local friction coefficient under par-
A. Pasanen et al. / Wear 267 (2009) 2200–2207
2201
Nomenclature a A c Ed Et p po P, Po q Qo Q r R Ra Rt x y z ı
radius of Hertzian contact (m) energy ratio (−) contact stick radius (m) hysteresis energy (J) total energy (J) contact pressure in z-direction (Pa) maximum Hertzian pressure (Pa) normal force (N) tangential traction in x-direction (Pa) tangential force amplitude (N) tangential force (N) radius of spherical contact (m) sphere radius of contact pad (m) surface roughness surface roughness coordinate along sliding direction coordinate normal to sliding direction depth coordinate measured tangential displacement amplitude (m) friction coefficient (−)
tial and mixed slip conditions are presented in reference [8]. The contact being studied consists of high speed steel with a specific thermal hardening against standard ball bearing steel. Comprehensive friction evolution of fretting contact in partial and gross slip conditions has been also made with titanium and aluminium alloys [9,10]. In general, high friction coefficients have been found in fretting contacts. However, little attention has been given to quenched and tempered steel, which is a commonly used material in heavy loaded conditions. In diesel engines this material is used in jointed components such as connecting rods, camshafts and crankshafts, whose loading conditions pose a potential risk of fretting. This study focuses on the experimental characterization of friction behavior of quenched and tempered steel in partial and gross slip conditions in fretting point contact.
Fig. 1. A schematic sphere on plane contact.
q(r) = po
r2 1− 2 a
1/2
c − po a
r2 1− 2 c
1/2 ,
0≤r≤c
(3b)
The partial slip condition in contact will occur when Q < P. In this case, the surfaces in the central zone of the circular contact (bounded by stick radius c) will stick together whereas the outer zone will slip as shown in Fig. 1. If Q = P, the tangential force is at its maximum and macroscopic sliding occurs between the surfaces. A detailed description of the formulation of the fretting problem is presented in Ref. [12]. 3. Experimental
2. Fretting point contact A sphere (body 1) and plane (body 2) make contact with the forces and coordinates as shown in Fig. 1. Hertzian normal contact pressure distribution p is assumed in non-conformal contact of two elastic spheres with smooth surfaces as follows:
p(x, y) = po 1 −
x2 y2 − 2 2 a a
1/2
(1)
where po is the maximum Hertzian pressure and a is the radius of a Hertzian circular contact. The total normal force P in z-direction is assumed to be constant (P = Po ), while the tangential force Q in xdirection is oscillating with an amplitude of ±Qo . Once a tangential force is introduced, some sliding or at least partial slip between the contacting surfaces will occur. Assuming a constant friction coefficient over the slip zone, the radius of the stick zone c and the tangential traction q caused by tangential motion is given inside the contact area where r < a, r = (x2 + y2 )1/2 , according to [11];
c =a 1−
Qo Po
q(r) = po
1/3
r2 1− 2 a
(2)
1/2 ,
c≤r≤a
(3a)
A Hertzian point contact configuration with a sphere against a plane was used in the experiments. A detailed description of the test device including the test specimen mounting and the application of bulk stress is presented in Ref. [13]. The principle of the fretting test device is shown in Fig. 2 and a short overview is given below. The test device has three similar sphere-on-plane test contacts running simultaneously. The plane is the test specimen, which can be loaded with tension stress. The strain-gauge was attached to every test specimen to measure this constant bulk stress. The three test specimens lie on the base structure, which is part of the frame of the device. The three contact pads with spherical contact profiles are joined to the plate of the lever arm (Fig. 2a), which is connected to a fixed shaft via a spherical plain thrust bearing without any clearance. The normal contact load is generated by the hydraulic cylinder through the bearing and the plate and this is measured continuously. The bearing allows the normal force to be distributed equally between the three contacts. The plate is connected to the electric shaker by the lever arm, which transfers the shaker head reciprocating motion into the rotational motion of the plate and test pads around the shaft center line. The tangential displacement amplitude and the motion frequency of the test pads can be adjusted and controlled accurately by the shaker control unit. The normal load, tangential force or displacement amplitude and bulk stress are adjusted and measured separately. The calibrations of the transducers were checked at regular intervals.
2202
A. Pasanen et al. / Wear 267 (2009) 2200–2207
Fig. 2. Principle of the test device and the contact situation.
The total tangential force induced by the three contacts with specified tangential displacement is measured continuously with a strain-gauge based transducer, which joins the plate and lever arm. The mean frictional force of the single contact can be obtained by dividing the total tangential force by the number of contacts. Tangential displacement is measured continuously with an eddy current probe as the relative movement between the fixed base structure of the specimen and the movable plate. This measured displacement includes possible sliding in contact together with compliance of the contact and test device. 3.1. Test specimens The contact pads and test specimens were made from quenched and tempered steel 34CrNiMo6. The spherical shapes of the pads were formed by grinding and polishing. The obtained geometry is shown in Fig. 3. The geometry and surface roughness of the contact pads were measured with a 3-D optical profilometer (Wyco NT 1100) for every test pad prior to the friction tests. The width of the sphere radiuses of the pads was 0.285 ± 0.015 m. The large radius of the sphere combined with reasonable contact pressure provided a contact area large enough for detailed examination of slip zone in partial slip
conditions. A large contact area diameter, when compared to the amplitude and wavelength of the surface roughness features, promotes the proper simulation of nominally flat parallel surfaces. Each test specimen’s width is 15 mm and thickness 5 mm. Two different topographies of plane surfaces were used in the friction tests as shown in Fig. 4. The first group of test specimens was polished to same the surface roughness as the test pads. The second group of the test specimens was ground into the direction of tangential motion (amplitude) induced by the test pads. The tensile bulk stress (tension) in the test specimen is exerted in the same direction. The measured surface roughness values of the test pads and the test specimens are presented in Table 1. The roughness of the test specimens was measured transversal to the direction of pad motion. The roughness of ground surfaces are in a same order of magnitude as the joints at risk of fretting in diesel engine applications. All test specimens belonging to each group were ground or/and polished at the same patch to obtain maximum similarity. 3.2. Test procedure The constant bulk stress was applied to the test specimens, after which the normal load was applied. The test was started by increasing the tangential displacement amplitude linearly with automatic operation from zero to the target value during the first 5000 cycles. Table 1 The surface roughness of the test pads and the test specimens. Contact body
Fig. 3. Geometry of the contact pad.
Pad (sphere) Specimen (polished) Specimen (ground)
Ra (m) 0.04–0.11 0.08–0.13 0.70–0.85
Rt (m) 2.2–2.9 2.5–3.3 5.0–7.5
A. Pasanen et al. / Wear 267 (2009) 2200–2207
2203
Fig. 4. Polished and ground surfaces of the test specimen.
Carefully controlled amplitude increase is important at the beginning of the test to prevent gross sliding of the surfaces. The target amplitude was kept constant during the rest of the test. The test time was set to one hour i.e. 144,000 cycles. The measured signals were saved to computer hard disc for further analysis. A hysteresis loop was created from the tangential force and displacement amplitude signals with a data collection frequency of 5000 Hz on each channel. This allows continuous follow-up of contact conditions during measurements. The measurements were carried out in the laboratory at room temperature (23–25 ◦ C). The relative humidity was not separately measured during these measurements, but the corresponding two-week measuring period showed the relative humidity of 20 ± 5%. The contact surfaces were cleaned with solvent beforehand.
Fig. 5. Typical contact trace after the one hour of testing.
can be calculated from Eq. (2) as follows; 3.3. Test matrix = The friction tests were performed with two normal force levels at different displacement amplitudes as shown in Table 2. At higher normal load level, friction was measured with six different tangential displacement amplitudes. The range of amplitudes was chosen to take account of partial and gross slip conditions. At lower normal load level, the tests were made with three amplitudes. The amplitude levels were chosen according to the pretest, in which a suitable operating window was sought and established. The same test matrix was carried out with both polished and ground specimens. The tensile bulk stress in the test specimens was set to 400 MPa in all tests. The frequency of the tangential motion related to Table 2 tests was 40 Hz. In addition, the friction test series was made in the frequency range 10–40 Hz in gross sliding conditions. 3.4. Evaluation of friction coefficient Three different methods were used for the evaluation of the friction coefficient in fretting point contact. Method 1 is based on wear marks in the partial slip zone. In this method, the contact radius a and stick radius c (Fig. 1) are measured from the contact trace. A testing time of one hour was used in the experiments. Typical contact trace after the test is shown in Fig. 5. Fig. 5 shows that one hour is long enough to have visible wear marks in the partial slip zone of the contact, but short enough to avoid excess wear, which may change the contact pressure distribution. Assuming a constant friction coefficient in slip zone and Hertzian pressure distribution in contact, the friction coefficient
1 1 − (c/a)
3
×
Q P
(4)
Normal force P and tangential force Q are obtained from measurements. The radius of the contact a and the stick zone c were determined as a mean value of the three contacts measured at the same time. This method is suitable for partial slip conditions with polished surfaces. It is based on visible contact trace, where all input parameters in Eq. (4) can be directly measured. However, this method is unable to detect instant friction values as a function of time. Application of this method to fretting fatigue measurements (crack initiation and growth) is also extremely difficult. Method 2 is based on measured tangential force–tangential displacement cycle, which is shown in Fig. 6. The complete tangential force–displacement cycle forms a hysteresis loop, which was measured on-line during the measurements with a data collection frequency of 5000 Hz on each channel. The area inside the hysteresis loop represents the work Ed done by the tangential force during the complete cycle and this energy is dissipated by reversal micro-slip in slip zone c ≤ r ≤ a [3]. The average of hysteresis energy and total energy Et (=4 × displacement amplitude × tangential force amplitude) were calculated afterwards from a one second sample (40 load cycles) of measured data every 24 s during a 15 min time interval at the end of the one hour test. As regards of fretting experiments, it is convenient to utilize the ratio A of the hysteresis energy and total energy as follows: A=
Ed Et
(5)
Table 2 Test matrix. Normal force P (N)
Hertzian mean and (maximum) pressure (MPa)
Measured tangential displacement amplitude (m)
1520 800
242 (363) 195 (293)
6 5
9 8
12 11
15
19
21
2204
A. Pasanen et al. / Wear 267 (2009) 2200–2207
Fig. 8. The tangential force Q and energy ratio A as a function of the tangential displacement amplitude ı, P = 1520 N, po = 363 MPa.
Fig. 6. Measured tangential force–tangential displacement cycle.
In sphere-on-plane contact, this ratio A can be presented as follows [8]:
A=
6 5
1 − (1 − (Q/P))
5/3
− (5Q/6P)
1 + (1 − (Q/P))
(Q/P) 1 − (1 − (Q/P))
2/3
2/3
accurate force and displacement signals with high data collection frequency. The friction coefficient value is very sensitive for the possible phase-shifts between these signals. These features were taken into account by using good quality sinusoidal tangential force controlled by an electric shaker unit and by using 5000 Hz frequency for data collection. This data collection frequency together with a frequency of 40 Hz for tangential motion resulted in every hysteresis loop having 125 measuring points, which was considered a reasonable value. In turn, the friction coefficient is very insensitive to the absolute value of tangential displacement. This is an essential feature because the measured displacement value is always affected to some extent by the compliance of the test device. Method 3 is based on classical friction definition, where the friction coefficient is obtained by dividing the tangential force by normal force. This method is valid only in gross sliding conditions.
(6) 4. Results and discussion The constant friction coefficient in slip zone was calculated from Eq. (6), where the ratio A, tangential force Q and normal force P were obtained from measurements. The maximum value of ratio A is 0.2, which can be obtained by substituting Q/(P) = 1 in Eq. (6). Below that value, partial slip conditions exist and Eq. (6) is valid for calculation. The A value of 0.2 represents the situation where the contact condition changes to gross sliding, which is also a very important feature to detect from the measurements. The high potential of this method is that it allows continuous follow-up of contact conditions and friction coefficient as a function of time i.e. load cycles. However, this method needs very clear and
4.1. Polished surfaces It was shown in Table 2 that the friction measurements were made with different load and tangential displacement levels including partial and gross slip conditions. Each test case (amplitude) included three parallel pad-specimen test contacts under similar operating conditions. The results with polished surfaces at the higher normal load level are presented in Figs. 7–9. The examples of the obtained contact traces with different displacement amplitudes are shown in Fig. 7.
Fig. 7. The contact traces with different tangential displacement amplitudes, P = 1520 N, po = 363 MPa. Upper row from left to right: (a) ı = 6 m, (b) ı = 9 m, (c) ı = 12 m. Lower row from left to right: (d) ı = 15 m, ı = 19 m, ı = 21 m. Scale 1 mm—the white beam at the bottom of the figure.
A. Pasanen et al. / Wear 267 (2009) 2200–2207
In Fig. 7, the three shortest displacement amplitude cases have a clear stick (unworn) zone at the center of the contact. They were interpreted as being in partial slip zone. The third case is already at the borderline of this zone, because only one of the three parallel contacts (shown in Fig. 7) has clearly entered the stick zone and in the rest of the contacts, the clear stick zone has already disappeared. When c/a < 0.4, the stick radius is already very sensitive to the tangential force, but the value of the stick radius has only a minor effect on the friction coefficient in Eq. (4). The contact stick zone decreases with increasing amplitude as theory would suggest in the partial slip zone. In the remaining amplitude cases, clear slip marks can already be seen across the whole contact surface, while wear increases with increasing amplitude. The amplitude cases 15 m and 19 m were classified as being in mixed zone, where the partial slip zone changes into gross slip zone, but the tangential force still increases with increasing amplitude. Pure gross sliding takes place in the longest amplitude case. The tangential force and the corresponding energy ratio for polished surfaces are shown in Fig. 8. Fig. 8 shows that the measured tangential force increases in conformity with increasing displacement amplitude at partial slip zone. In this zone, the energy ratio is under 0.2 which is also indicative of partial slip conditions. At mixed slip zone, tangential force still increases with increasing amplitude, but finally it becomes constant and the energy ratio reaches a value of 0.2, also indicative of the onset of gross sliding conditions. It is important to note, that these friction results are based on preset time interval. The friction dependence on load cycles is discussed later. The friction coefficient as a function of the tangential displacement amplitude for polished surfaces is shown in Fig. 9. The friction coefficient in Fig. 9 was determined by the contact trace method (Eq. (4)) and by the energy ratio method (Eq. (6)) in partial slip conditions. The methods show good correspondence. The friction coefficient in pure gross sliding condition was determined in the classical way from the ratio Q/P. The result is in accordance with the results measured with the energy ratio method. The on-line energy method seems to successfully correspond to the other methods for the detection of the friction coefficient. The results in Fig. 9 show that the friction coefficient increases with increasing displacement amplitude at partial slip condition. This results in a different trend than that produced with aluminium alloys, which shows a constant friction coefficient in the partial slip zone [10]. The highest friction coefficient is reached at the mixed slip zone where partial slip changes to gross slip resulting in a friction coefficient up to 1.3. This level of friction induces very high tangential traction in contact and, in consequence, a high risk of cracking, i.e., fretting fatigue. Calculation of the stress field at the contact surface revealed that the maximum Von Mises stresses at the mixed and gross slip zones are already in the range of yield stress of the test material. This may also explain the slightly higher increase in friction coefficient between the amplitudes 12 m and 15 m.
Fig. 9. The friction coefficient as a function of the tangential displacement amplitude ı, P = 1520 N, po = 363 MPa.
2205
Fig. 10. The tangential force Q and energy ratio A as a function of the tangential displacement amplitude ı for ground (black) and polished (red) surfaces, P = 1520 N, po = 363 MPa. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
Calculation of the theoretical tangential displacement amplitude of the smooth contact using the measured tangential force and friction coefficient indicated that the calculated tangential displacement amplitude is smaller than that of the corresponding measured one, which results from the compliance of the test device. 4.2. Ground surfaces Tests were also made with ground (rough) surfaces using the same test matrix (Table 2) that used for polished surfaces. The measurements were performed with similar displacement amplitudes for both surface types. This measured amplitude includes the compliance of the contact, which may be different for polished and ground surfaces. The results for the tangential force and the corresponding energy ratio are shown in Fig. 10. The results in Fig. 10 show that the tangential force is the same with three shortest amplitude cases for polished and ground surfaces. However, the tangential force for ground surfaces is lower than for polished surfaces at the longest amplitudes. The contact trace of ground surface is shown in Fig. 11. Fig. 11 shows that contact has to take place only at the upper parts of the ground (wavy) surface. An important point is that there is not longer a clear stick zone. This means that mixed slip condition at least at the end of the test is already present in the second shortest amplitude case. In the shortest amplitude case, signs of stick zones
Fig. 11. The contact trace of ground surface, ı = 9 m, P = 1520 N, po = 363 MPa. Scale 1 mm—the black beam at the bottom of the figure.
2206
A. Pasanen et al. / Wear 267 (2009) 2200–2207
Fig. 12. Friction coefficient as a function of load cycles, ı = 6 m (left) and 15 m (right), P = 1520 N, po = 363 MPa, polished surface.
can be observed. The energy ratio indicates that gross sliding is achieved in the highest amplitude case (19 m). By assuming the gross sliding conditions, the friction coefficient was calculated directly from ratio Q/P. A maximum friction coefficient value of about 1.0 was obtained in the longest amplitude case. It is obvious that ground surfaces promote a lower maximum friction coefficient together with mixed/gross sliding in operating conditions used in this study. Further study is needed to explain exactly this difference, which may be related to true contact area and wearing of the surface profile. Modeling of rough contact properties is a topic for future research. 4.3. Lower normal load level Some tests were also made with lower load level as shown in Table 2. All three test cases were already close to or at the mixed slip zone, which prevented the use of contact trace for calculation of friction coefficient. As in the earlier case, the tests with ground surfaces caused mixed or gross sliding already with the shortest amplitude. The maximum friction coefficient value estimated from ratio Q/P for polished surface was about 1.2 and for ground surfaces about 1.1. The maximum friction coefficient in gross sliding conditions is much the same in lower and higher load cases for polished and ground surfaces. 4.4. Time dependence of friction coefficient The foregoing chapters deal with the friction coefficient, which was obtained in the contact trace method case after one hour of testing and in the energy ratio case as the mean value from a 15 min time interval at the end of the test. The on-line energy method also allows follow-up of the trend of instant friction coefficient during the measurements. The results are shown in Fig. 12. The friction coefficient is obtained by calculating its mean value during one second (40 cycles) at every 100 s.
Fig. 12 shows that the friction coefficient has its maximum value just after the displacement amplitude has been automatically raised to the target value. After that it decreases and settles at a certain value (Fig. 12a), which is typical for clear partial slip conditions. At mixed slip zone, the one hour testing time may already be too short for complete stabilization of the friction coefficient as shown in Fig. 12b. This limited testing time was applied in order to minimize the risk of macroscopic wearing of the slip zone with polished surfaces as shown in Fig. 5. However, friction behavior shows that some form of microscopic change must occur during contact such as the initial wear of surface asperity tips despite the polished surfaces. The severity of the friction coefficient peak at the beginning of the test seems to be dependent on the operating parameters employed. The friction peak is especially promoted by operation in the mixed slip zone with polished surfaces. This friction coefficient peak may have a role in crack initiation in fretting contact, because it causes high cyclic tangential traction in fretting contact. 4.5. Frequency dependence of friction coefficient In all the earlier tests the frequency of the tangential motion was 40 Hz. This high frequency is needed to achieve a reasonable testing time in the fretting fatigue tests. However, this frequency is fairly high when it is compared, for example, to the corresponding fretting frequencies in diesel engines (6–20 Hz). For this reason, the test series was also made where this frequency varied between 10 and 40 Hz. The tests were performed under operating conditions with gross sliding and high load to ascertain, for example, possible temperature effects during contact. The friction coefficient was calculated from the ratio Q/P and the results are presented in Fig. 13. The Fig. 13 shows that friction coefficient increases slightly with increased frequency. The inspection of surfaces revealed no major differences in contact traces between the different frequency cases. 5. Conclusions Tangential traction caused by friction in contacting surfaces is a major factor in fretting fatigue that increases stress levels and leads to a reduction in fatigue life. Friction in fretting contact was studied in partial and gross slip conditions. Measurements were made with sphere-on-flat contact geometry on quenched and tempered steel. Friction was evaluated on-line from measured tangential load-displacement cycle and, after the tests, from contact trace. The tangential motion was controlled with constant displacement amplitude and the corresponding tangential force was measured. The following conclusions were drawn:
Fig. 13. Friction coefficient as a function of frequency of tangential motion, ı = 20 m, P = 1520 N, po = 363 MPa, polished surface.
- The on-line energy method seems to correspond positively to the other methods for the detection of friction coefficient, provided that measured tangential force and displacement signals
A. Pasanen et al. / Wear 267 (2009) 2200–2207
-
-
-
-
-
-
are accurate. However, further tests are needed in a wider range of operating conditions. The highest friction coefficient is reached at the mixed slip zone where partial slip changes to gross sliding. A maximum friction coefficient up to 1.3 was measured with polished surfaces. Friction coefficient increases with increasing displacement amplitude in partial and mixed slip zone with polished surfaces Ground surfaces promote a lower maximum friction coefficient and mixed/gross slip already appears at the shortest displacement amplitudes in similar operating conditions in comparison to polished surfaces. The maximum friction coefficient in gross sliding conditions is much the same in lower and higher load cases for polished and ground surfaces. The friction coefficient is dependent on load cycles. It has its maximum value at the beginning of the test, just after the displacement amplitude has been increased to the target value. The maximum friction coefficient is especially promoted by operation in mixed slip zone with polished surfaces. The frequency of tangential motion in a range between 10 and 40 Hz has no major effect on the friction coefficient under gross sliding conditions. Overall understanding of friction coefficient behavior was achieved. This knowledge will be used in a numerical fretting model for the evaluation of fretting fatigue crack initiation.
Acknowledgements This study is a part of a FREFA (Fretting Fatigue in Diesel Engineering) project which is being carried out in collaboration with
2207
Wärtsilä Finland Oy, Tampere University of Technology and Helsinki University of Technology. The authors are grateful for the financial support provided by Wärtsilä Finland Oy and Finnish Funding Agency for Technology and Innovation. References [1] R.B. Waterhouse (Ed.), Fretting Fatigue, Applied Science Publishers, Barking, 1981, p. 244. [2] D.A. Hills, D. Novell, Mechanics of Fretting Fatigue, Kluwer Academic Publishers, Dordrecht, 1994, p. 236. [3] K.L. Johnson, Contact Mechanics, Cambridge University Press, 1985, p. 452. [4] A. Lehtovaara, R. Rabb, Fretting fatigue crack initiation for a smooth spherical contact—a parameter study, Finnish J. Tribol. 25 (2006) 31–40. [5] A. Lehtovaara, R. Rabb, A numerical model for the evaluation of fretting fatigue crack initiation in rough point contact, Wear 264 (2008) 750–756. [6] R. Rabb, P. Hautala, A. Lehtovaara, Fretting fatigue in diesel engineering, Paper No: 76, Proc. of 25th CIMAC Congress, Vienna, May 21–24, 2007. [7] S. Fouvry, Ph. Kapsa, L. Vincent, Developments of fretting sliding criteria to quantify the local friction coefficient evolution under partial slip condition, Tribol. Ser. 34 (1998) 161–172. [8] D. Dini, D. Nowell, Prediction of the slip zone friction coefficient in flat and rounded contact, Wear 254 (2003) 364–369. [9] B. Alfredsson, A. Cadario, A study on fretting friction evolution and fretting fatigue crack initiation for a spherical contact, Int. J. Fatigue 26 (2004) 1037–1052. [10] H. Proudhon, S. Fouvry, J.-Y. Buffière, A fretting crack initiation prediction taking into account the surface roughness and the crack nugleation process volume, Int. J. Fatigue 27 (2005) 569–579. [11] R.D. Mindlin, Compliance of elastic bodies in contact, J. Appl. Mech. 16 (1949) 259–268. [12] A. Lehtovaara, R. Rabb, A numerical model for the calculation of fretting fatigue crack initiation for a smooth spherical contact, Finnish J. Tribol. 25 (2006) 23–30. [13] A. Pasanen, S. Järvisalo, A. Lehtovaara, R. Rabb, Development of a test device for the evaluation of fretting in point contact, Lubrication Sci. 21 (2009) 41–52.
Contents lists available at ScienceDirect
Wear journal homepage: www.elsevier.com/locate/wear
Friction behavior of quenched and tempered steel in partial and gross slip conditions in fretting point contact A. Pasanen a , A. Lehtovaara a,∗ , R. Rabb b , P. Riihimäki a a b
Mechanics and Design, Tampere University of Technology, P.O. Box 589, 33101 Tampere, Finland Research & Development, Wärtsilä Finland Oy, P.O. Box 244, FI-65101 Vaasa, Finland
a r t i c l e
i n f o
Article history: Received 30 September 2008 Received in revised form 20 March 2009 Accepted 24 March 2009 Available online 7 April 2009 Keywords: Friction Fretting fatigue Fretting wear Partial slip
a b s t r a c t Tangential traction caused by friction in contacting surfaces is a major factor in fretting fatigue that increases stress levels and leads to a reduction in fatigue life. Friction in fretting contact was studied in partial, mixed and gross slip conditions on quenched and tempered steel. Measurements were made with sphere-on-plane contact geometry for polished and ground surfaces. Friction was evaluated from on-line energy ratio and, after the tests, from wear marks. A maximum friction coefficient of over 1.0 was measured at mixed slip zone with polished surfaces, whereas ground surfaces promote lower values in similar operating conditions. The friction coefficient dependence on load cycles and loading frequency is also presented and briefly discussed. The friction data and understanding thus gained is to be used for evaluation of crack initiation with the numerical fretting fatigue model. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Fretting may occur between any two contacting surfaces where short amplitude reciprocating sliding is present over a large number of cycles. This oscillatory movement can take place at the micrometer level, even without gross sliding of the contacting surfaces. This causes fretting wear of the surfaces and fretting fatigue, which can lead to a rapid decrease in fatigue life. Fretting wear is related to surface degradation processes and it can be detected by the appearance of wear debris. The appearance and severity of fretting fatigue is essentially dependent on the stress field on a contact (sub)surface caused by external bulk and contact loading. This stress field, affected by the oscillatory movement of the contacting surfaces, promotes crack nucleation. An extensive description of the fretting phenomenon and its associated contact mechanics is given in Refs. [1–3]. Fretting risks are known to be high in industrial machine components such as medium speed diesel engines, where the contact surfaces have to transfer high tractions. Fretting often occurs in contacts which are designed to be nominally fixed, such as interference fits and screw joints. Fretting fatigue may cause hazardous and unexpected damage in machine components, because the appearing nominal stress levels can be low and the damage that initiates on the inside of the contact cannot be detected by normal visual inspection without opening the joint.
∗ Corresponding author. Tel.: +358 3 311511; fax: +358 3 31152307. E-mail address: arto.lehtovaara@tut.fi (A. Lehtovaara). 0043-1648/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2009.03.047
Proper design, material properties, different kinds of palliatives and surface treatments have been considered as ways to eliminate or control fretting. The promotion of compact and reliable calculation and design rules for fretting requires both modelling and experimentation, due to the complexity of the problem. Modelling provides a detailed understanding of the stress fields and the estimated cracking risk based on multi-axial failure criteria at contacting surfaces and contributes to the design and evaluation of experimental fretting fatigue tests [4–6]. The oscillatory tangential movement of the contacting bodies is the basis of the fretting phenomenon. This causes the tangential traction into the contact, which is known to have a very strong impact on the stress field and thus on cracking risk. The level of the tangential traction is firmly controlled by friction between contacting surfaces and therefore the determination of the friction coefficient in fretting contact is a crucial task. This input value is one of the main uncertainties when the cracking risk of the fretting contact is evaluated with numerical fretting models. The vast majority of the fretting studies have been conducted on gross sliding conditions, where the whole contact is sliding. In such cases, the friction coefficient can be defined simply by dividing the tangential force by the normal force. However, fretting fatigue and corresponding crack formation is known to take place primarily in partial or mixed slip conditions, where tangential force is less than or just reaching the product of friction coefficient and normal force. This complicates the determination of the friction coefficient. Prediction of the slip zone friction coefficient by using measured mean friction coefficient is given in reference [7]. A detailed approach for measurement and analysis of local friction coefficient under par-
A. Pasanen et al. / Wear 267 (2009) 2200–2207
2201
Nomenclature a A c Ed Et p po P, Po q Qo Q r R Ra Rt x y z ı
radius of Hertzian contact (m) energy ratio (−) contact stick radius (m) hysteresis energy (J) total energy (J) contact pressure in z-direction (Pa) maximum Hertzian pressure (Pa) normal force (N) tangential traction in x-direction (Pa) tangential force amplitude (N) tangential force (N) radius of spherical contact (m) sphere radius of contact pad (m) surface roughness surface roughness coordinate along sliding direction coordinate normal to sliding direction depth coordinate measured tangential displacement amplitude (m) friction coefficient (−)
tial and mixed slip conditions are presented in reference [8]. The contact being studied consists of high speed steel with a specific thermal hardening against standard ball bearing steel. Comprehensive friction evolution of fretting contact in partial and gross slip conditions has been also made with titanium and aluminium alloys [9,10]. In general, high friction coefficients have been found in fretting contacts. However, little attention has been given to quenched and tempered steel, which is a commonly used material in heavy loaded conditions. In diesel engines this material is used in jointed components such as connecting rods, camshafts and crankshafts, whose loading conditions pose a potential risk of fretting. This study focuses on the experimental characterization of friction behavior of quenched and tempered steel in partial and gross slip conditions in fretting point contact.
Fig. 1. A schematic sphere on plane contact.
q(r) = po
r2 1− 2 a
1/2
c − po a
r2 1− 2 c
1/2 ,
0≤r≤c
(3b)
The partial slip condition in contact will occur when Q < P. In this case, the surfaces in the central zone of the circular contact (bounded by stick radius c) will stick together whereas the outer zone will slip as shown in Fig. 1. If Q = P, the tangential force is at its maximum and macroscopic sliding occurs between the surfaces. A detailed description of the formulation of the fretting problem is presented in Ref. [12]. 3. Experimental
2. Fretting point contact A sphere (body 1) and plane (body 2) make contact with the forces and coordinates as shown in Fig. 1. Hertzian normal contact pressure distribution p is assumed in non-conformal contact of two elastic spheres with smooth surfaces as follows:
p(x, y) = po 1 −
x2 y2 − 2 2 a a
1/2
(1)
where po is the maximum Hertzian pressure and a is the radius of a Hertzian circular contact. The total normal force P in z-direction is assumed to be constant (P = Po ), while the tangential force Q in xdirection is oscillating with an amplitude of ±Qo . Once a tangential force is introduced, some sliding or at least partial slip between the contacting surfaces will occur. Assuming a constant friction coefficient over the slip zone, the radius of the stick zone c and the tangential traction q caused by tangential motion is given inside the contact area where r < a, r = (x2 + y2 )1/2 , according to [11];
c =a 1−
Qo Po
q(r) = po
1/3
r2 1− 2 a
(2)
1/2 ,
c≤r≤a
(3a)
A Hertzian point contact configuration with a sphere against a plane was used in the experiments. A detailed description of the test device including the test specimen mounting and the application of bulk stress is presented in Ref. [13]. The principle of the fretting test device is shown in Fig. 2 and a short overview is given below. The test device has three similar sphere-on-plane test contacts running simultaneously. The plane is the test specimen, which can be loaded with tension stress. The strain-gauge was attached to every test specimen to measure this constant bulk stress. The three test specimens lie on the base structure, which is part of the frame of the device. The three contact pads with spherical contact profiles are joined to the plate of the lever arm (Fig. 2a), which is connected to a fixed shaft via a spherical plain thrust bearing without any clearance. The normal contact load is generated by the hydraulic cylinder through the bearing and the plate and this is measured continuously. The bearing allows the normal force to be distributed equally between the three contacts. The plate is connected to the electric shaker by the lever arm, which transfers the shaker head reciprocating motion into the rotational motion of the plate and test pads around the shaft center line. The tangential displacement amplitude and the motion frequency of the test pads can be adjusted and controlled accurately by the shaker control unit. The normal load, tangential force or displacement amplitude and bulk stress are adjusted and measured separately. The calibrations of the transducers were checked at regular intervals.
2202
A. Pasanen et al. / Wear 267 (2009) 2200–2207
Fig. 2. Principle of the test device and the contact situation.
The total tangential force induced by the three contacts with specified tangential displacement is measured continuously with a strain-gauge based transducer, which joins the plate and lever arm. The mean frictional force of the single contact can be obtained by dividing the total tangential force by the number of contacts. Tangential displacement is measured continuously with an eddy current probe as the relative movement between the fixed base structure of the specimen and the movable plate. This measured displacement includes possible sliding in contact together with compliance of the contact and test device. 3.1. Test specimens The contact pads and test specimens were made from quenched and tempered steel 34CrNiMo6. The spherical shapes of the pads were formed by grinding and polishing. The obtained geometry is shown in Fig. 3. The geometry and surface roughness of the contact pads were measured with a 3-D optical profilometer (Wyco NT 1100) for every test pad prior to the friction tests. The width of the sphere radiuses of the pads was 0.285 ± 0.015 m. The large radius of the sphere combined with reasonable contact pressure provided a contact area large enough for detailed examination of slip zone in partial slip
conditions. A large contact area diameter, when compared to the amplitude and wavelength of the surface roughness features, promotes the proper simulation of nominally flat parallel surfaces. Each test specimen’s width is 15 mm and thickness 5 mm. Two different topographies of plane surfaces were used in the friction tests as shown in Fig. 4. The first group of test specimens was polished to same the surface roughness as the test pads. The second group of the test specimens was ground into the direction of tangential motion (amplitude) induced by the test pads. The tensile bulk stress (tension) in the test specimen is exerted in the same direction. The measured surface roughness values of the test pads and the test specimens are presented in Table 1. The roughness of the test specimens was measured transversal to the direction of pad motion. The roughness of ground surfaces are in a same order of magnitude as the joints at risk of fretting in diesel engine applications. All test specimens belonging to each group were ground or/and polished at the same patch to obtain maximum similarity. 3.2. Test procedure The constant bulk stress was applied to the test specimens, after which the normal load was applied. The test was started by increasing the tangential displacement amplitude linearly with automatic operation from zero to the target value during the first 5000 cycles. Table 1 The surface roughness of the test pads and the test specimens. Contact body
Fig. 3. Geometry of the contact pad.
Pad (sphere) Specimen (polished) Specimen (ground)
Ra (m) 0.04–0.11 0.08–0.13 0.70–0.85
Rt (m) 2.2–2.9 2.5–3.3 5.0–7.5
A. Pasanen et al. / Wear 267 (2009) 2200–2207
2203
Fig. 4. Polished and ground surfaces of the test specimen.
Carefully controlled amplitude increase is important at the beginning of the test to prevent gross sliding of the surfaces. The target amplitude was kept constant during the rest of the test. The test time was set to one hour i.e. 144,000 cycles. The measured signals were saved to computer hard disc for further analysis. A hysteresis loop was created from the tangential force and displacement amplitude signals with a data collection frequency of 5000 Hz on each channel. This allows continuous follow-up of contact conditions during measurements. The measurements were carried out in the laboratory at room temperature (23–25 ◦ C). The relative humidity was not separately measured during these measurements, but the corresponding two-week measuring period showed the relative humidity of 20 ± 5%. The contact surfaces were cleaned with solvent beforehand.
Fig. 5. Typical contact trace after the one hour of testing.
can be calculated from Eq. (2) as follows; 3.3. Test matrix = The friction tests were performed with two normal force levels at different displacement amplitudes as shown in Table 2. At higher normal load level, friction was measured with six different tangential displacement amplitudes. The range of amplitudes was chosen to take account of partial and gross slip conditions. At lower normal load level, the tests were made with three amplitudes. The amplitude levels were chosen according to the pretest, in which a suitable operating window was sought and established. The same test matrix was carried out with both polished and ground specimens. The tensile bulk stress in the test specimens was set to 400 MPa in all tests. The frequency of the tangential motion related to Table 2 tests was 40 Hz. In addition, the friction test series was made in the frequency range 10–40 Hz in gross sliding conditions. 3.4. Evaluation of friction coefficient Three different methods were used for the evaluation of the friction coefficient in fretting point contact. Method 1 is based on wear marks in the partial slip zone. In this method, the contact radius a and stick radius c (Fig. 1) are measured from the contact trace. A testing time of one hour was used in the experiments. Typical contact trace after the test is shown in Fig. 5. Fig. 5 shows that one hour is long enough to have visible wear marks in the partial slip zone of the contact, but short enough to avoid excess wear, which may change the contact pressure distribution. Assuming a constant friction coefficient in slip zone and Hertzian pressure distribution in contact, the friction coefficient
1 1 − (c/a)
3
×
Q P
(4)
Normal force P and tangential force Q are obtained from measurements. The radius of the contact a and the stick zone c were determined as a mean value of the three contacts measured at the same time. This method is suitable for partial slip conditions with polished surfaces. It is based on visible contact trace, where all input parameters in Eq. (4) can be directly measured. However, this method is unable to detect instant friction values as a function of time. Application of this method to fretting fatigue measurements (crack initiation and growth) is also extremely difficult. Method 2 is based on measured tangential force–tangential displacement cycle, which is shown in Fig. 6. The complete tangential force–displacement cycle forms a hysteresis loop, which was measured on-line during the measurements with a data collection frequency of 5000 Hz on each channel. The area inside the hysteresis loop represents the work Ed done by the tangential force during the complete cycle and this energy is dissipated by reversal micro-slip in slip zone c ≤ r ≤ a [3]. The average of hysteresis energy and total energy Et (=4 × displacement amplitude × tangential force amplitude) were calculated afterwards from a one second sample (40 load cycles) of measured data every 24 s during a 15 min time interval at the end of the one hour test. As regards of fretting experiments, it is convenient to utilize the ratio A of the hysteresis energy and total energy as follows: A=
Ed Et
(5)
Table 2 Test matrix. Normal force P (N)
Hertzian mean and (maximum) pressure (MPa)
Measured tangential displacement amplitude (m)
1520 800
242 (363) 195 (293)
6 5
9 8
12 11
15
19
21
2204
A. Pasanen et al. / Wear 267 (2009) 2200–2207
Fig. 8. The tangential force Q and energy ratio A as a function of the tangential displacement amplitude ı, P = 1520 N, po = 363 MPa.
Fig. 6. Measured tangential force–tangential displacement cycle.
In sphere-on-plane contact, this ratio A can be presented as follows [8]:
A=
6 5
1 − (1 − (Q/P))
5/3
− (5Q/6P)
1 + (1 − (Q/P))
(Q/P) 1 − (1 − (Q/P))
2/3
2/3
accurate force and displacement signals with high data collection frequency. The friction coefficient value is very sensitive for the possible phase-shifts between these signals. These features were taken into account by using good quality sinusoidal tangential force controlled by an electric shaker unit and by using 5000 Hz frequency for data collection. This data collection frequency together with a frequency of 40 Hz for tangential motion resulted in every hysteresis loop having 125 measuring points, which was considered a reasonable value. In turn, the friction coefficient is very insensitive to the absolute value of tangential displacement. This is an essential feature because the measured displacement value is always affected to some extent by the compliance of the test device. Method 3 is based on classical friction definition, where the friction coefficient is obtained by dividing the tangential force by normal force. This method is valid only in gross sliding conditions.
(6) 4. Results and discussion The constant friction coefficient in slip zone was calculated from Eq. (6), where the ratio A, tangential force Q and normal force P were obtained from measurements. The maximum value of ratio A is 0.2, which can be obtained by substituting Q/(P) = 1 in Eq. (6). Below that value, partial slip conditions exist and Eq. (6) is valid for calculation. The A value of 0.2 represents the situation where the contact condition changes to gross sliding, which is also a very important feature to detect from the measurements. The high potential of this method is that it allows continuous follow-up of contact conditions and friction coefficient as a function of time i.e. load cycles. However, this method needs very clear and
4.1. Polished surfaces It was shown in Table 2 that the friction measurements were made with different load and tangential displacement levels including partial and gross slip conditions. Each test case (amplitude) included three parallel pad-specimen test contacts under similar operating conditions. The results with polished surfaces at the higher normal load level are presented in Figs. 7–9. The examples of the obtained contact traces with different displacement amplitudes are shown in Fig. 7.
Fig. 7. The contact traces with different tangential displacement amplitudes, P = 1520 N, po = 363 MPa. Upper row from left to right: (a) ı = 6 m, (b) ı = 9 m, (c) ı = 12 m. Lower row from left to right: (d) ı = 15 m, ı = 19 m, ı = 21 m. Scale 1 mm—the white beam at the bottom of the figure.
A. Pasanen et al. / Wear 267 (2009) 2200–2207
In Fig. 7, the three shortest displacement amplitude cases have a clear stick (unworn) zone at the center of the contact. They were interpreted as being in partial slip zone. The third case is already at the borderline of this zone, because only one of the three parallel contacts (shown in Fig. 7) has clearly entered the stick zone and in the rest of the contacts, the clear stick zone has already disappeared. When c/a < 0.4, the stick radius is already very sensitive to the tangential force, but the value of the stick radius has only a minor effect on the friction coefficient in Eq. (4). The contact stick zone decreases with increasing amplitude as theory would suggest in the partial slip zone. In the remaining amplitude cases, clear slip marks can already be seen across the whole contact surface, while wear increases with increasing amplitude. The amplitude cases 15 m and 19 m were classified as being in mixed zone, where the partial slip zone changes into gross slip zone, but the tangential force still increases with increasing amplitude. Pure gross sliding takes place in the longest amplitude case. The tangential force and the corresponding energy ratio for polished surfaces are shown in Fig. 8. Fig. 8 shows that the measured tangential force increases in conformity with increasing displacement amplitude at partial slip zone. In this zone, the energy ratio is under 0.2 which is also indicative of partial slip conditions. At mixed slip zone, tangential force still increases with increasing amplitude, but finally it becomes constant and the energy ratio reaches a value of 0.2, also indicative of the onset of gross sliding conditions. It is important to note, that these friction results are based on preset time interval. The friction dependence on load cycles is discussed later. The friction coefficient as a function of the tangential displacement amplitude for polished surfaces is shown in Fig. 9. The friction coefficient in Fig. 9 was determined by the contact trace method (Eq. (4)) and by the energy ratio method (Eq. (6)) in partial slip conditions. The methods show good correspondence. The friction coefficient in pure gross sliding condition was determined in the classical way from the ratio Q/P. The result is in accordance with the results measured with the energy ratio method. The on-line energy method seems to successfully correspond to the other methods for the detection of the friction coefficient. The results in Fig. 9 show that the friction coefficient increases with increasing displacement amplitude at partial slip condition. This results in a different trend than that produced with aluminium alloys, which shows a constant friction coefficient in the partial slip zone [10]. The highest friction coefficient is reached at the mixed slip zone where partial slip changes to gross slip resulting in a friction coefficient up to 1.3. This level of friction induces very high tangential traction in contact and, in consequence, a high risk of cracking, i.e., fretting fatigue. Calculation of the stress field at the contact surface revealed that the maximum Von Mises stresses at the mixed and gross slip zones are already in the range of yield stress of the test material. This may also explain the slightly higher increase in friction coefficient between the amplitudes 12 m and 15 m.
Fig. 9. The friction coefficient as a function of the tangential displacement amplitude ı, P = 1520 N, po = 363 MPa.
2205
Fig. 10. The tangential force Q and energy ratio A as a function of the tangential displacement amplitude ı for ground (black) and polished (red) surfaces, P = 1520 N, po = 363 MPa. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
Calculation of the theoretical tangential displacement amplitude of the smooth contact using the measured tangential force and friction coefficient indicated that the calculated tangential displacement amplitude is smaller than that of the corresponding measured one, which results from the compliance of the test device. 4.2. Ground surfaces Tests were also made with ground (rough) surfaces using the same test matrix (Table 2) that used for polished surfaces. The measurements were performed with similar displacement amplitudes for both surface types. This measured amplitude includes the compliance of the contact, which may be different for polished and ground surfaces. The results for the tangential force and the corresponding energy ratio are shown in Fig. 10. The results in Fig. 10 show that the tangential force is the same with three shortest amplitude cases for polished and ground surfaces. However, the tangential force for ground surfaces is lower than for polished surfaces at the longest amplitudes. The contact trace of ground surface is shown in Fig. 11. Fig. 11 shows that contact has to take place only at the upper parts of the ground (wavy) surface. An important point is that there is not longer a clear stick zone. This means that mixed slip condition at least at the end of the test is already present in the second shortest amplitude case. In the shortest amplitude case, signs of stick zones
Fig. 11. The contact trace of ground surface, ı = 9 m, P = 1520 N, po = 363 MPa. Scale 1 mm—the black beam at the bottom of the figure.
2206
A. Pasanen et al. / Wear 267 (2009) 2200–2207
Fig. 12. Friction coefficient as a function of load cycles, ı = 6 m (left) and 15 m (right), P = 1520 N, po = 363 MPa, polished surface.
can be observed. The energy ratio indicates that gross sliding is achieved in the highest amplitude case (19 m). By assuming the gross sliding conditions, the friction coefficient was calculated directly from ratio Q/P. A maximum friction coefficient value of about 1.0 was obtained in the longest amplitude case. It is obvious that ground surfaces promote a lower maximum friction coefficient together with mixed/gross sliding in operating conditions used in this study. Further study is needed to explain exactly this difference, which may be related to true contact area and wearing of the surface profile. Modeling of rough contact properties is a topic for future research. 4.3. Lower normal load level Some tests were also made with lower load level as shown in Table 2. All three test cases were already close to or at the mixed slip zone, which prevented the use of contact trace for calculation of friction coefficient. As in the earlier case, the tests with ground surfaces caused mixed or gross sliding already with the shortest amplitude. The maximum friction coefficient value estimated from ratio Q/P for polished surface was about 1.2 and for ground surfaces about 1.1. The maximum friction coefficient in gross sliding conditions is much the same in lower and higher load cases for polished and ground surfaces. 4.4. Time dependence of friction coefficient The foregoing chapters deal with the friction coefficient, which was obtained in the contact trace method case after one hour of testing and in the energy ratio case as the mean value from a 15 min time interval at the end of the test. The on-line energy method also allows follow-up of the trend of instant friction coefficient during the measurements. The results are shown in Fig. 12. The friction coefficient is obtained by calculating its mean value during one second (40 cycles) at every 100 s.
Fig. 12 shows that the friction coefficient has its maximum value just after the displacement amplitude has been automatically raised to the target value. After that it decreases and settles at a certain value (Fig. 12a), which is typical for clear partial slip conditions. At mixed slip zone, the one hour testing time may already be too short for complete stabilization of the friction coefficient as shown in Fig. 12b. This limited testing time was applied in order to minimize the risk of macroscopic wearing of the slip zone with polished surfaces as shown in Fig. 5. However, friction behavior shows that some form of microscopic change must occur during contact such as the initial wear of surface asperity tips despite the polished surfaces. The severity of the friction coefficient peak at the beginning of the test seems to be dependent on the operating parameters employed. The friction peak is especially promoted by operation in the mixed slip zone with polished surfaces. This friction coefficient peak may have a role in crack initiation in fretting contact, because it causes high cyclic tangential traction in fretting contact. 4.5. Frequency dependence of friction coefficient In all the earlier tests the frequency of the tangential motion was 40 Hz. This high frequency is needed to achieve a reasonable testing time in the fretting fatigue tests. However, this frequency is fairly high when it is compared, for example, to the corresponding fretting frequencies in diesel engines (6–20 Hz). For this reason, the test series was also made where this frequency varied between 10 and 40 Hz. The tests were performed under operating conditions with gross sliding and high load to ascertain, for example, possible temperature effects during contact. The friction coefficient was calculated from the ratio Q/P and the results are presented in Fig. 13. The Fig. 13 shows that friction coefficient increases slightly with increased frequency. The inspection of surfaces revealed no major differences in contact traces between the different frequency cases. 5. Conclusions Tangential traction caused by friction in contacting surfaces is a major factor in fretting fatigue that increases stress levels and leads to a reduction in fatigue life. Friction in fretting contact was studied in partial and gross slip conditions. Measurements were made with sphere-on-flat contact geometry on quenched and tempered steel. Friction was evaluated on-line from measured tangential load-displacement cycle and, after the tests, from contact trace. The tangential motion was controlled with constant displacement amplitude and the corresponding tangential force was measured. The following conclusions were drawn:
Fig. 13. Friction coefficient as a function of frequency of tangential motion, ı = 20 m, P = 1520 N, po = 363 MPa, polished surface.
- The on-line energy method seems to correspond positively to the other methods for the detection of friction coefficient, provided that measured tangential force and displacement signals
A. Pasanen et al. / Wear 267 (2009) 2200–2207
-
-
-
-
-
-
are accurate. However, further tests are needed in a wider range of operating conditions. The highest friction coefficient is reached at the mixed slip zone where partial slip changes to gross sliding. A maximum friction coefficient up to 1.3 was measured with polished surfaces. Friction coefficient increases with increasing displacement amplitude in partial and mixed slip zone with polished surfaces Ground surfaces promote a lower maximum friction coefficient and mixed/gross slip already appears at the shortest displacement amplitudes in similar operating conditions in comparison to polished surfaces. The maximum friction coefficient in gross sliding conditions is much the same in lower and higher load cases for polished and ground surfaces. The friction coefficient is dependent on load cycles. It has its maximum value at the beginning of the test, just after the displacement amplitude has been increased to the target value. The maximum friction coefficient is especially promoted by operation in mixed slip zone with polished surfaces. The frequency of tangential motion in a range between 10 and 40 Hz has no major effect on the friction coefficient under gross sliding conditions. Overall understanding of friction coefficient behavior was achieved. This knowledge will be used in a numerical fretting model for the evaluation of fretting fatigue crack initiation.
Acknowledgements This study is a part of a FREFA (Fretting Fatigue in Diesel Engineering) project which is being carried out in collaboration with
2207
Wärtsilä Finland Oy, Tampere University of Technology and Helsinki University of Technology. The authors are grateful for the financial support provided by Wärtsilä Finland Oy and Finnish Funding Agency for Technology and Innovation. References [1] R.B. Waterhouse (Ed.), Fretting Fatigue, Applied Science Publishers, Barking, 1981, p. 244. [2] D.A. Hills, D. Novell, Mechanics of Fretting Fatigue, Kluwer Academic Publishers, Dordrecht, 1994, p. 236. [3] K.L. Johnson, Contact Mechanics, Cambridge University Press, 1985, p. 452. [4] A. Lehtovaara, R. Rabb, Fretting fatigue crack initiation for a smooth spherical contact—a parameter study, Finnish J. Tribol. 25 (2006) 31–40. [5] A. Lehtovaara, R. Rabb, A numerical model for the evaluation of fretting fatigue crack initiation in rough point contact, Wear 264 (2008) 750–756. [6] R. Rabb, P. Hautala, A. Lehtovaara, Fretting fatigue in diesel engineering, Paper No: 76, Proc. of 25th CIMAC Congress, Vienna, May 21–24, 2007. [7] S. Fouvry, Ph. Kapsa, L. Vincent, Developments of fretting sliding criteria to quantify the local friction coefficient evolution under partial slip condition, Tribol. Ser. 34 (1998) 161–172. [8] D. Dini, D. Nowell, Prediction of the slip zone friction coefficient in flat and rounded contact, Wear 254 (2003) 364–369. [9] B. Alfredsson, A. Cadario, A study on fretting friction evolution and fretting fatigue crack initiation for a spherical contact, Int. J. Fatigue 26 (2004) 1037–1052. [10] H. Proudhon, S. Fouvry, J.-Y. Buffière, A fretting crack initiation prediction taking into account the surface roughness and the crack nugleation process volume, Int. J. Fatigue 27 (2005) 569–579. [11] R.D. Mindlin, Compliance of elastic bodies in contact, J. Appl. Mech. 16 (1949) 259–268. [12] A. Lehtovaara, R. Rabb, A numerical model for the calculation of fretting fatigue crack initiation for a smooth spherical contact, Finnish J. Tribol. 25 (2006) 23–30. [13] A. Pasanen, S. Järvisalo, A. Lehtovaara, R. Rabb, Development of a test device for the evaluation of fretting in point contact, Lubrication Sci. 21 (2009) 41–52.